Gauge Fixing in QFT and the Dressing Field Method

TL;DR

This paper explores the Dressing Field Method in quantum gauge theories, showing that gauge fixing procedures like Faddeev-Popov and unitary gauge are specific applications of this method within the path integral formalism.

Contribution

It adapts the Dressing Field Method to the functional path integral formalism, providing a geometric perspective on gauge fixing in quantum field theories.

Findings

Gauge fixing is an instance of the Dressing Field Method.

Reinterpretation of Faddeev-Popov gauge fixing and unitary gauge.

Extension of DFM to infinite-dimensional field spaces.

Abstract

In this paper, we revisit the Dressing Field Method (DFM) in the context of Quantum (Gauge) Field Theories (QFT). In order to adapt this method to the functional path integral formalism of QFT, we depart from the usual differential geometry approach used so far to study the DFM which also allows to tackle the infinite dimension of the field spaces. Our main result is that gauge fixing is an instance of the application of the DFM. The Faddeev-Popov gauge fixing procedure and the so-called unitary gauge are revisited in light of this result.